Extraction of Solids with Liquids Multiple and Countercurrent Extraction EDW. A. RAVENSCROFT Abbott Laboratories, North Chicago, Ill.
M
ANY mathematical formulas (I, 3, 6, 8, 9)
A complete graphical solution of problems involving the multiple and continuous countercurrent extraction of solids with liquids is presented including the case of extraction with varying entrainment. The latter condition has not been discussed in the literature heretofore. The solution of a practical problem of this type is also presented.
Multiple extraction, or the treatment of one lot of solids repeatedly with fresh menstruum. Continuous countercurrent extraction, or the moving of the sludge countercurrent to the menstruum through a tank or series of tanks. Batch countercurrent extraction, or the treatment of each lot of solids with successively weaker batches of menstruum-that is, in countercurrent sequence.
have been presented for the solution of extraction problems. Most of them are Irrespective of the method of extraction used, it will simsomewhat special in application and do not present a simple plify the mathematical considerations involved if all quantitreatment when the data known are different from those for ties of solvent, etc., are considered on the basis of one unit which the formulas were designed. Graphical solutions of solids treated. The nomenclature used in the following soluextraction problems have also been presented (2, 4, 6, 7 ) . tions is therefore based on one pound of insoluble solids. These solutions, however, have not been worked out primarily Multiple Extraction for the extraction of solids with liquids and are not readily adaptable to these problems. Therefore, a completely graphiThe nomenclature used is as follows: cal solution applicable to nearly all types of extraction of solids with liquids has been developed, and found to be rapid z = composition of menstruum, pounds extractant per pound menstruum and convenient. I n addition, it solves some types of probm = menstruum adhering to the solids (i. e., the entrainment), lems not discussed heretofore and permits us to visualize pounds readily the effect of changing the terminal conditions of a M = menstruum removed from the tank after a given wash, given system. pounds E i = extractant present in solids initially, pounds It will be assumed throughout this discussion that the Si = solvent present in solids initially, pounds method of extraction employed involves a thorough mixing of zi = composition of menstruum present in solids initially the solvent with the finely divided solids to give a complete Whencexi = Ei solution of all of the extractant present. An equilibrium Ei S, condition results in which the resulting menstruum is of uniMa = menstruum used for each wash, pounds form concentration, both that free to be removed from the zo = composition of fresh menstruum used in each wash, sludge and that entrained by the sludge and carried by it to pounds W = waste (i. e., residual extractant present in sludge after the the next tank or operation. final wash), pounds Heretofore, it has been customary to assume further that Whence W = Wq the amount of menstruum entrained by the solids is constant. In many cases considerable error may be introduced by negFigure 1 represents the operations performed by the nth lecting to take into consideration the variation in entrainment wash in systems of this type, and the following equations may that may occur. This variation is particularly noticeable be written: when the viscosity and density of the menstruum increases appreciably as the concentration of extractant present beMenstruum balance: M O m,-i = Mn (1) comes larger. It is generally possible experimentally to deExtractant balance: M O ~ Omn--lxn-l = mnzn Mnzn ( 2 ) termine the entrainment per unit of solids treated as a funcIn most extraction problems of this type, E, and 8,are tion of the concentration of extractant in the menstruum by known from the analysis of the untreated solids; the entrainmixing together various mixtures and noting the results. ment, m, has been determined experimentally as a f(z); and Each of the graphical methods here presented starts with a Mo and zo are assumed to see what W will become after a graph of this function. Thus, these methods are more gengiven number of washes. erally applicable than those presented heretofore. Obviously This problem is solved graphically as follows: On a set of if the entrainment is constant, the graph becomes a straight x, y coordinates, as shown in Figure 2, plot the entrainment line which simplifies the balance of the construction somewhat curve y = m = f(z). The values of Si and Ei are laid off but does not affect its accuracy. above the x axis on the line 2 = 1.0. The line z = xi is loThree of the commonest types of extraction of solids with &)z, which intersects cated by drawing the line y = (Ed liquids will be discussed : 851 ~
+
+ +
+
+
+
INDUSTRIAL AND ENGINEERING CHEMISTRY
852
Befors
t i o n of xi. The horizontal line y = -Ma and the vertical line x = zo are also drawn. Points A and 3 a r e connected a s shown. Line A 3 crosses the x axis a t z = $1. This can be proved from
Wash:
w = mn-,xn-, After Wash :
W = m,xn
++
++
+ +
Rearranging: MOZO %(E$ Si) = x ~ ( M o Ei Si) From (1): M O ~ OEi = a ( M 1 ml) which is the extractant balance similar to Equation 2 but written for the first wash. and the From the intersection of the vertical line z = entrainment curve y = m, another triangle is constructed as shown and the value of xz determined. This construction is repeated for the desired number of washes. After finding the value of xf2the intersection of the line x = xf with the entrainment curve is projected over to the line x = 1.0 and the line y = ~ J isX drawn. The value of W is read from the intersection of this line with the line x = x/ as shown in Figure 2. If the quantity of wash menstruum, Ma, varies from wash t o wash, the construction can be made by using an appropriate set of lines for y = -Mo. If pure solvent is used for washing, xo = 0 and the triangulation is performed on the y axis. Also, if the entrainment is constant, y = m becomes a horizontal straight line and the triangulation becomes simpler again. The construction in this case is a graphical solution of the Hawley formula for multiple extraction (1).
General Considerations in Countercurrent Extraction Irrespective of the details of the method of countercurrent extraction used, several mathematical considerations of the
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VOL. 28, NO. 7
system as a whole may be written. As before, the following nomenclature is assumed on the basis of one pound of insoluble solids: 1440 = fresh menstruum fed to the system, pounds zo = composition of fresh menstruum, pounds extractant per pound menstruum M p = product menstruum leaving system, pounds m, = menstruum leaving the system adhering t o the exhausted solids (i. e., the entrainment), pounds xp = composition of product menstruum, pounds extractant per pound menstruum zm = composition of menstruum leaving the system adhering to the exhausted solids, pounds extractant per pound menstruum 8, = solvent, if any, present in untreated solids fed to system, pounds E/ = extractant in untreated solids entering system as feed, pounds q = composition of menstruum in untreated solids fed to system, pounds extractant per pound menstruum
Whence
xj
Ef = ___
+
E. Sf Referring to Figure 3, the following material balances may be written :
+ + +
+
Menstruum balance: MO E/ Sf = M , m, Extractant balance: E, MOZO = M,zp mwxw
+
(3) (4)
I n most extraction problems, E/ and Sf are known from the analysis of the untreated solids, and xo from the analysis of t h e fresh menstruum. The enM MPXP trainment, m , of t h e s l u d g e is k n o w n as a f h ) . The product Countercurrent is known from the value of Ef and the Extraction percentage of re~ystem covery desired; xw and m, may then b e determined from the entrainmwxw ment f u n c t i o n . The three unFIGURE3. DIAGRAM OF COUNTERCURknowns leftRENT EXTRACTION n a m e l y , xp, Mo, and M , may be calculated from Equations 3 and 4 for any assumed value of one of them. Often a definite composition of the h a 1 menstruum is desired-i. e., x p is known; or again it may be desired to determine the results if a certain amount of fresh menstruum is used-i. e., Mu is known; and finally it may be desired to produce a definite amount of product menstruum -i. e., m pis known. Graphically these cases may be quickly solved as follows: On a set of z,y coordinates as in Figure 4,draw the curve y = m = f(x) and y = mx = xf(s). By laying off the distances SJ and EJ above the x axis on the vertical line x = 1.0, the line y = (E, &)x is easily constructed. Draw the horizontal line y = Ef. The value of xf may be read as shown, since by definition it is the value of 2: which makes (E, &)a: = E/. By definition the horizontal line y = m d W intersects the curve y = mx a t x = x,. The vertical line x = x w intersects the curve y = m at y = mu. Assuming the value of M Ois known, lay it off down the line 1: = 1.0 as shown, thereby locating point A . The value of M p may then be read directly since, from the relation of the line segments along x = 1.0, we may write:
&Gc,
I
/
I
2
+
+
M o - m, = Mp - E/ - Sf xi FIQURE 2. GRAPHICAL SOLUTION OF MULTIPLE EXTRACTION which is Equation 3 in transposed form.
x x f
a
x,
Ed,
JULY, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
853
ing graphical solutions for the number of tanks required in continuous and batch countercurrent extractions.
Continuous Countercurrent Extraction Extraction systems of this type may be represented as in Figure 5 . Dorr thickeners hooked up for countercurrent washing form such a system. The workings of such a system are well known. Examining the nth tank in detail, we find that sludge is entering this tank from the n 1 tank carrying with it menstruum represented by mn+l. The composition of this menstruum is represented by xnf l expressed as pounds of extractant per pound of menstruum. We find also that wash menstruum is entering this tank from the n - 1 tank. The number of pounds of this menstruum is represented by iM,- and its composition by xn- These two flows of material mix and, after reaching equilibrium, the menstruum in the tank has composition xn. The pounds of wash menstruum leaving this tank to go to the n - 1 tank are represented by M,, and the menstruum carried into tank n - 1 with the sludge is represented by mn. Equations 3 and 4 apply and may be used to determine the terminal conditions graphically as described heretofore. Referring again to Figure 5 , we may write: n - 1: Menstruum balance around tanka 1 . mn M O = M,-I mw (5) Extractant balance: M n - 1 z n - 1 = m,pn M O ~-OmwzW (6)
+
A
FIGURE4. TERMINAL COXDITIONSIN COUNTERCURRENT EXTRACTIONS
Calculate the value of M 0 x 3 from the kno& value of xo and and draw the horizontal line y = the assumed value of Mo, m , s w- M ~ x o . Draw a line from A to the origin. Its slope is evidently - ( M o - mu) and its equation is y = - ( M o- mw)x. This line will hereafter be referred to as the menstruum line. It intersects x = xf a t point B where y = -(Mo- mw)xj. Draw a line through B having a y intercept equal to E/. From Figure 4 the slope of this line is evidently
-_ Ef + _(Mo- mUJh =
-
5
9 - ( M o - m,) XI
+
Now, at y
=
xwmw- M O X O this , becomes mwxw- Mozo
=
+ E/
-M,z
and from Equation 4, -M,x xp
MPxp
x
=
Thus the value of z pmay be read as shown. From the geometry of Figure 4 it is evident that we could have started with an assumed value of M , or xp and solved for the other unknowns. Since Equations 3 and 4 apply to all countercurrent extraction systems, the above construction will have a similar broad application. It will be used as the starting point in the follow- - - - -.- -.
- - -- - - - - -
.-
rm.&.& I
. . ..
I I(
[ mar*, I L- - - - - - _ - - _ _ _ - _ _ _ FIQURE
5.
I
mn X"
+n'" J%*l
... .
+
Mn-~xn (mw - Mo)x, - ( m w ~ w- MOZO) Mn-lzn-1 Whence: Mn-l(xn - xnn--l)= ( M o- mw)xn-I- (mwzw- MOZO)
Substituting and rearranging: xn-1
-
+
(mwzw- M o ~ o ) ( M o- m d z n mnzn - (mwzw- Mozd
(7)
Equation 7 contains only the compositions xn and xn-l and is the basis of the construction used to determine the number of tanks required. Figure 6 is a set of x,y coordinates on which have been drawn the curves y = m, y = mx, the vertical line x = 1.0, and the horizontal line y = m a w - Moxa. The menstruum line is then constructed as described previously. Starting with a given composition line, xn, draw the horizontal line y = mnxn having a y intercept at C. The menstruum line crosses the composition line x = xn a t F. Draw the diagonal line CF, which intersects the horizontal line ?J = m d w - Moxa at D. Draw a vertical composition line through this point. From the similar triangles CBD and DEF we may write: DE EF = BD
+
Bv the nature of the construction, EF = ( m d W- M O X O ) . (2,- mw)xnand B D = mDxn- ' ( m d , M O X O ) Assuming C B = x , - ~ , then D E = x n - Xn-1, and by substituting all these values in the preceding equation we obtain Equation 7. Hence, C B = x,,-~. Therefore, to determine the number of tanks required in a given problem, this construction is repeated starting a t x = xp until a value of x equal to or less than xw is obtained. less The than number the of number such constructions of tanks required will for be conone
r',
I _I
DETAILED DIAGRAM
+
Substituting the value of m, from Equation 5 :
xn - zn-l
the equation of
+
+
=
+ 8,) - (AVO- m,)
-(-%
which from Equation 3 simplifies to -M,; the line is therefore : 21 = - MPx E/
.. .
O F COUNTERCURRENT EXTRACTION
tinuous countercurrent extraction. This construction, when once mastered, does not take very long and is much shorter than a
1
INDUSTRIAL AND ENGINEERING CHEMISTRY
854
yt
I
VOL. 28, NO. 7
veloped may be considered as holding per unit of time or per unit of solids treated, depending upon which basis is more convenient in a given case.
Batch Countercurrent Extraction A system of this type is illustrated in Figure 7. The percolation of cascara bark as commonly carried out by pharmaceutical manufacturers is an example of this system. A , B, C, and D represent percolators. A, B, and C contain drugs, A being the most nearly exhausted. Each is flooded with menstruum that came from the preceding percolator. The steps of a cycle of operation are as follows:
FIGURE 6. PARTIAL SOLUTION OF CONTINUOUS COTJNTERCURRENT EXTRACTION
series of algebraic solutions to Equations 5 and 6. Since the entrainment is an empirical function of x, there can be no short cut to this rather tedious mathematical procedure. In case the variation in entrainment is negligible from tank to tank, the curve y = mx becomes a straight line and the triangulation just described is performed with equal ease. In the case where the entering solids contain no solvent, the vertical line x = xf coincides with the line x = 1.0. In the case where the entering menstruum contains no extractant, xo = 0, and the entrainment line ?J = m x W - Moxa coincides with the line y = m d w ; the triangulation is otherwise unaffected. I n some cases point A may be found to lie above the x axis ( M o
